Modelling the temperature suitability for the risk of West Nile Virus establishment in European Culex pipiens populations

Abstract Increases in temperature and extreme weather events due to global warming can create an environment that is beneficial to mosquito populations, changing and possibly increasing the suitable geographical range for many vector‐borne diseases. West Nile Virus (WNV) is a flavivirus, maintained in a mosquito–avian host cycle that is usually asymptomatic but can cause primarily flu‐like symptoms in human and equid accidental hosts. In rare circumstances, serious disease and death are possible outcomes for both humans and horses. The main European vector of WNV is the Culex pipiens mosquito. This study examines the effect of environmental temperature on WNV establishment in Europe via Culex pipiens populations through use of a basic reproduction number (R0) model. A metric of thermal suitability derived from R0 was developed by collating thermal responses of different Culex pipiens traits and combining them through use of a next‐generation matrix. WNV establishment was determined to be possible between 14°C and 34.3°C, with the optimal temperature at 23.7°C. The suitability measure was plotted against monthly average temperatures in 2020 and the number of months with high suitability mapped across Europe. The average number of suitable months for each year from 2013 to 2019 was also calculated and validated with reported equine West Nile fever cases from 2013 to 2019. The widespread thermal suitability for WNV establishment highlights the importance of European surveillance for this disease and the need for increased research into mosquito and bird distribution.


Additional Methodological Details R0 Equation Derivation:
The equation for 0 is calculated from a next generation matrix adapted from Vogels et al. (2017), where ℎ indicates the number of mosquitoes that acquire WNV from an infected host (bird) and ℎ indicates the number of hosts (avian, equid or human) that acquire infection from a mosquito. It is assumed that no host to host or mosquito to mosquito transmission takes place. Subscript T indicates that a trait is temperature dependant. Birds are the primary route of WNV introduction as mammalian hosts do not cause onward transmission. Hence the traits included in the ℎ equation pertain only to avian hosts and are as follows: the mosquito biting rate, proportional to the reciprocal of the gonotrophic (egg-laying) cycle ( ); the host preference, or probability that the mosquito bloodmeal is from a bird ( ); mosquito density ( ); bird density ( ) and the infectious period of the bird, included as the inverse of recovery rate ( ). These five traits combine to give the number of bites that a WNV positive bird will receive whilst infectious. The probability of transmission from bird to mosquito ( ) is also included.
ℎ includes: the mosquito biting rate ( ); the probability of transmission from mosquito to host ( ); the mosquito mortality rate ( ), also used as the mosquito 'recovery' rate; and the extrinsic incubation period, which is the number of days after feeding on an infectious bird that a mosquito becomes infectious ( ). The combination − , derived from the Ross-Macdonald equation, gives the probability that a mosquito will survive the extrinsic incubation period (Smith et al., 2012).
Combination of the next generation matrix into an equation for the value of 0 is calculated via the method described by Diekmann and Heesterbeek (2000). Vector Competence (bc T ) was extracted from the data as the highest proportion of mosquitoes with disseminated infection for each temperature. Mosquitoes with disseminated infection are thought to reasonably approximate those transmitting WNV (Turell et al., 2001). This also provided us with the corresponding number of days post infectious feed ( ).

Trait Trait Description Sources used
Biting Rate (a T ) Reciprocal of the gonotrophic cycle (time between feeding and egg laying) was taken to be proportional to bite rate. Madder et al. (1983) Host Preference (φ) Probability that the mosquito blood meal is a bird. Weighted mean was calculated based on mosquito sample size in each of the studies. Recovery Rate of Birds (r b ) was for passerine species only. Birds with viraemia greater than 10 5 PFU/mL were considered infectious to Culex pipiens (Turell et al., 2000). A mean for the two studies weighted on sample size was calculated.
Fecundity (F T ) data was not readily available; data points were taken from Shocket et al. (2020) originally published in Li et al. (2017). No weightings were available and data was from the subspecies Culex pipiens pallens.
Mosquito development rate (D T ) was presented separately for egg and larval stages. Egg development rate was from Madder et al. (1983). Larval development rate (LDR) and egg development rate (EDR) were combined as follows:

Sensitivity analysis:
A sensitivity analysis is carried out to assess how the traits and overall ( ) are affected by changes in temperature. This is done by differentiating ( ) with respect to temperature using the following equation: Here is the partial derivative of ( ) with respect to trait and is the partial derivative of with respect to temperature. The contribution of individual traits to the ( ) temperature sensitivity can be assessed using these components of Equation S.2, for example the temperature sensitivity arising through biting rate ( ) is shown by the equation . This influence of each trait on the sensitivity of ( ) to temperature is then plotted in Figure 3 in the main text alongside the overall sensitivity of ( ).

Additional Results
This section contains a table showing the fit for the thermal response curves for each trait (Table S2), the plot of our suitability metric against temperature ( Figure S1) as well as additional maps and validation. In particular, the maps for each month in 2020 showing the calculated ( ) ( Figure S2); an aggregated map showing the number of months Europe spends in permissive temperatures for WNV establishment ( ( )>0) in 2020 ( Figure S3); and the aggregated maps for each year of 2013 to 2019 for the number of months with higher suitability ( ( ) ≥ 0.5), with the cases from each year plotted on top ( Figure S4). For the validation, we also provide the number of reported equine WNV cases in 2013-2019 located in areas of varying numbers of months with permissive temperatures for WNV ( Figure S5); and a distribution of the number of months of suitability for all cells in Europe compared against those cells with cases, for both the higher suitability threshold ( Figure S6) and the permissive threshold ( Figure S7). Egg development rate ( ) Linear 0.031 -0.21 *The corrected AIC was slightly lower for a linear fit, however upon visual inspection the data shows a clear unimodal trend and a quadratic curve was selected to improve biological representation.